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ABSTRACT
The local structure of undirected multigraphs under two random multigraph models is analyzed and compared. The first model generates multigraphs by randomly coupling pairs of stubs according to a fixed degree sequence so that edge assignments to vertex pair sites are dependent. The second model is a simplification that ignores the dependency between the edge assignments. It is investigated when this ignorance is justified so that the simplified model can be used as an approximation, thus facilitating the structural analysis of network data with multiple relations and loops. The comparison is based on the local properties of multigraphs given by marginal distribution of edge multiplicities and some local properties that are aggregations of global properties.
Acknowledgments
I would like to thank Ove Frank for his insightful comments and valuable suggestions during the preparation of this manuscript. I would also like to thank the anonymous reviewers for their constructive comments that help improve the manuscript.
Funding
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007- 2013)/ERC Grant Agreement n. 319209.